What is the degree of x^5+1-3x^9-2x

this polynomial has a degree of 9.

The degree of a polynomial is the highest power of the unknown with a non-zero coeficient.

This expresion has unknown x raised to the 5th, 4th, 9th and 1st power

(x=x1)

with coeficients of : 1,-3,+3 and - 2 respectively. So the highest power (i. e. the degree of the polynomial) is 9.